Dustin Penner scored at 17 minutes and 42 seconds of overtime to complete a five-game triumph in the Western Conference finals.
Penner's pass set up Jeff Carter for a shot from the right circle that Mike Smith stopped but the rebound fell to Penner and he lifted the winning shot into the net.
The Kings won for the 12th time in 14 post-season games and set a play-off record by winning their 10th consecutive road game this post-season.
Taylor Pyatt had given Phoenix the lead after 4:20 of the first period but Anze Kopitar levelled it up at 11:13.
Marc-Antoine Pouliot put Phoenix back in front in the second period before the Kings took control through Drew Doughty and Mike Richards.
Keith Yandle levelled levelled the game up and after a scoreless third period it was left to Penner to send the Kings to the final with his winner 17:42 into overtime.